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The phrase "primary factor that" is correct and can be used in written English.
It is typically used to introduce the main reason or cause in a sentence. Here is an example: "The primary factor that contributed to their success was their strong teamwork."
Exact(52)
It is the primary factor that makes such kind of document images hard to be recognized.
It is obvious that continuous working time (CWT) is the primary factor that affects human reliability in this scenario.
The distance between the quencher-fluorophore pair is the primary factor that determines the quenching efficiency of the probe [21].
Casey described the extended time accommodation as "game changing" and the primary factor that "kept me in nursing school".
Adsorbent particle size may be the primary factor that influences drug release from various SSNEDDS formulations (Amrutkar et al. 2014).
Results show that the temperature is the primary factor that influences the steam gasification reaction of rice husk char.
Similar(8)
But for most postmenopausal women, hormone-related changes are the primary factors that interfere with sexual satisfaction.
There are two primary factors that determine the monthly payment on a mortgage, the principal balance (ie, what the mortgage is worth), and the interest rate.
And the four primary factors that beget hits — beyond monumental talent — are all in Jeter's favor.
What are the primary factors that influence FinTech over time?
Flood control and navigation are primary factors that control how the river is managed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com